A method of assembly a brush seal between two components having confronting adjacent surfaces, such as the stator and rotor of a gas turbine, comprises providing a slot in one of the components which slot opens through the confronting surface of that component to face the other component. A flexible brush seal element having a plurality of metallic bristles is pushed into the slot so that the free ends of the bristles project from said surface of the one component. The element is then held in position in the slot by means of an anchoring strip pushed into the slot so as to bear on a wall thereof and also on the brush seal element, the anchoring strip typically being of a malleable metal.